Measuring risk in investments

Measuring risk in investments

Measuring risk in investments

General definition of risk, corporate risk

The risk represents a certain level of uncertainty.

It is a something one bears and is the outcome of uncertainty.

However professional understanding of it in the fields of business economics and finance and the subsequent management of identified risks requires to distinguish between these two terms. First of all the risk differs from the uncertainty in the way that is measurable and thereby it is possible to determine the probability of deviation of the real state of the expected one and the size of this deviation (e. g. the probability that the expected cash flow will differ from real cash generated by a specific investment project is 20%, the probability that the business partner will default on interest and principal payments on the borrowing is 5% etc.). The uncertainty is a broader term and it is connected with such deviations of real state from the expected, whose probability or size are not measurable. Except that the risk is rather subjectively perceived category than the uncertainty. Based on said, in general the risk

…represents a state in which the number of possible future events exceeds the number of events that will actually occur, and some measure of probability can be attached to them.

To this definition it must be also added, that any risk has a time horizon, meaning that evolves over time.

However in the business practise, the general definition of the risk is not sufficient and thereby it is complemented by other facts, which are determined by the nature of the risk. In the field of the entrepreneurship (from a holistic point of view), as the general type of risk the corporate risk may be considered. It goes together with the basic target of each entrepreneurship –

.. a maximizing of the company’s market value for its owners

(accepting the limitation deriving from interest of other stakeholders, e.g. creditors, investors, business partners, employees, customers, state etc.). Then the corporate risk is a probability that the real company’s market value will differ from its expected value (by accepting both positive and negative deviations from the expected value). If the element of this risk was ignored (when corporate strategy is being framed and tactical projects are being implemented) the loss could be unimaginable.

The corporate risk has to be considered as a very comprehensive, resulting from different kinds of individual business decisions (e.g. in the field of the products and services, which company sells or provides, decisions on marketing mix, decisions on which market operates in, decisions on which investments should be undertaken, decisions if the investments should be financed by own or borrowed capital, etc.), risk factors in the internal and external business environment, and consisting many other partial risks, which can affect each other. The business practise, as well as the theoretical seeing of the corporate risk, categorizes these risks from different perspectives, but in the context of this article, meaning in the context of investment activities, investments valuation and finally investment decision-making process, authors restrict the area of interest to the risk involved in the investment activities, specifically concerning risks in the investment finance area – equity risk and counterparty default risk.

Investments and risks

The investment activity is seeing as a driver of the economy (in general) and then it is logic that it must to be an integral part of any business. The appropriate investment decisions are able to support the future development of the company and in the final they also support to meet the main target of the entrepreneurship. Then it is logic that the company (in the position of investor) prefers the highest-return investments, but it will behave rationally only when it takes into account as well the level of investment’s riskiness. It means that

… instead of relying purely on button-line profits, each investment should be evaluated based on its returns (cash flows) as well as its risks.

The investment activity is associated with many risks mainly because of long-term nature of investments and existence of the uncertainty. The uncertainty in the investment process represents the impossibility of reliable determination of future factors that affected investment cash flows. The overall (basic) risk refers to any kind of investments is that the expected investment’s cash flows will differ from the expected (predicted), in other words – that the investment will not be able to generate expected cash flow and negatively influence the development of company’s value and wealth of its owners and investors (with the meaning of providers of debts – creditors). The riskiness of investment is determined by the riskiness of its cash flows and usually it is reflected in the hurdle rate, which is seen as the minimal rate of return on the undertaken investment required by investors in general meaning (e.g. managers, owners – if the governance structure differs from ownership structure, creditors). The higher the riskiness of the investment is, the higher hurdle rate will be required by them. The hurdle rate is often used as the discount rate, too, meaning that it is incorporated in the process of determination of the present value of the future expected investment’s cash flows and thus it is taken into account within the process of the investment valuation. It is important to note, that the hurdle rate required by different groups of investors is usually different, because each who participates in the investment may perceive its risk in varying intensity (risk aversion).

The risks that are linked with investment activities, more specifically with financial investment activities (it will be abstracted from the investments into real assets), may be classified in many ways. In the context of this paper, the criterion if the financial investment involves any promised returns has been set as the basic. Based on it, if the investment does not involves any promised cash flow, investor will face to so-called equity risk. If the investments will involve promised cash flows (e.g. cash flows on bonds – coupon payments, payments of principal and interest on provided loan, payment of bill of exchange), investor, or better say creditor, will face to the counterparty default risk.

Equity risk

The equity risk belongs into the group of financial risks. It is involved in buying or taking an equity position in a company and it is characterized for such kind of financial investments, where no cash flows are promised to the investor. In the position of investor is an owners or stockholders (individual or institutional including other corporations and state) that primary profit from the fact that company is profitable (they are involved in the company’s profit), and from the fact that the company’s market value is growing (the value of capital, which they invested in the company has been growing – the market value of company’s share has been growing).

The equity risk, which the investor faces to, is given by fluctuation in shares, which results in fluctuating returns, especially in the case when the market price of shares is depreciating. The future returns – future price of shares may be derived from the historical data and usually are seen as a specific statistical probability distribution. Then the basic statistical characteristics of that distribution are measures of risk, in other words upside potential and downside risk on returns from shares.

There are many factors that determine the equity risk, but usually they are classified as: company-specific (or firm-specific) and marketwide factors. The risk that is caused by the first group of factors affects just one or few companies and their shares  values (or a specific sector with no significant impact on other sector). It is known as company-specific risk and it is diversifiable. The diversification of investment portfolio, in other words investing into more than one kind of assets, shares or do more than one investment project, can help investor to reduce exposure to the company-specific risk. If the investor diversifies, then each investment in the portfolio is much smaller percentage of the overall portfolio that would be in case, if the investor did not diversify. Than any change in the value of that individual investment (or small group of investments – it depends on the portfolio’s structure) will influence the investor’s overall diversified portfolio in a smaller degree than the undiversified investment portfolio (with the same individual investment), which is exposed to the company-specific risk in full range. Then savings, which may accrue from the portfolio diversification, are statistically represented by the function of the coefficient of correlation in returns between investments in the investment portfolio.

The risk caused by the second group of factors has a wide scope of action, and thus influence all equity investments, companies, markets and economic sectors, although in different degrees. It is known as a market risk and is nondiversifiable, which means that by diversification of portfolio the investor cannot eliminate it. The market risk includes complex of risk factors, such as changes of inflation, interest rates, changes in the taxation, changes of exchange rates, or political risk etc.

In the scientific literature there has been presented many more or less different models that are used in the corporate finance for measuring market risk. All models have common that as the basic way how to measure the risk of the analysed investment into firm or individual company’s stocks statistically is the usage of variance in actual returns around the expected ones. Next it is assumed that the marginal investor prefers to keep a diversified portfolio, thus models will reward and price just the market risk.

In practise, among the most frequently used models belong: capital asset pricing model (CAPM), arbitrage pricing model (APM), multifactor model (MM), and proxy model (PM; knows as regression model, too). The first three models use common measure of market risk – the parameter (or factor) beta looking at historical data. Based on Mun beta is defined as

… the undiversifiable, systematic risk of a financial asset.

The higher beta means the higher market risk of assumed investment. All three models differ in a way how they identify (quantify) the value of beta factor and if they assume with multiple sources of market risk – the CAPM assumes just with one (market risk is captured in the market portfolio), other assumes with more than one beta. The fourth model does not use factor beta as the measure of market risk, but indirect measures so-called proxies, which are common for investments with consistently high returns that are considered to be more risky than other investments, e.g. price-book value ratio, market capitalization etc. All models differ, except others, in the way how they perceive the market risk, too. In the following table, the definition of market risk and betas based on principles of all mention models are presented.

In closing of this classification, it should be noted also risks (or factors that arise these risks), which fall in a grey area, depending on how many investments (market value of shares) they are able to effect. Thereby they cannot be exactly given into the group of company-specific risk or market risk.

The comparison of models measuring market risk

The CAPM The APM The MF The PM
Market Risk Risk added by any investment (asset) to the market portfolio. Risk is given by mutltiple sources and exposures of any asset to market variables. Risk exposures of any investment to macro- economic factors. Risk captured by the characteristics of high- return investments that are considered as indirect measures, co- called proxy variables.
Measure of Market Risk Parameter Beta

Beta of assets relative to market portofolio (Beta measured against the market porfolio).

Parameter Beta

Beta of asset relatives to unspecified market factors (Beta mesuared against multipe unspecified factors of market risk).

Parameter Beta

Beta of asset relatives to specified macro- economic factors (Beta measured against multiple specified macroeconomic factors).

Indirect variables (proxy variables) Equation relating returns to proxies.

Default risk

The counterparty default risk (default risk, direct credit risk) belongs into the group of credit risks that is the sub-group of financial risk. The credit risk, in a general meaning, represents a counterparty default risk that

… involves inability or unwillingness of counterparty to meet its commitments in relation to lending, trading, hedging, settlement and other financial transactions.

Except the default risk to this group belongs: large credit exposure risk, risk of default arising from the application of the agreed financial instrument (e.g. bank guarantee, insurance, letter of credit, derivate contract etc.) – credit equivalent exposure risk, and risk due to deficiencies in the final settlement of contracts – settlement risk.

In the context of investments, investment decision-making process and investment valuation this type of risk is related to the investments with cash flows, which are promised when the investment is made. In the strict sense, the default risk concerns mainly the situation when any economic entity (in general, e.g. individual, company, bank, other financial but non-bank institution, state) gets into the position of creditor (lender), who borrows money to other economic entity, so-called borrower. It particularly goes on the financial activities related to the provision of bank loans, financial loans and investment in the purchase of debt securities, mainly bonds. The borrower is obliged to return the money in a specified way, time and amount. Then the default risk is a state when the borrower does not meet its liabilities over the life of loan – defaults on principal, interest or coupon payments.

The main task is to evaluate (measure) the credit quality of potential or already existing borrower, which represents the likelihood that the promised cash flows will not be delivered to the creditor as will be or was agreed. The higher is the probability of borrower’s failure, the more the creditor is exposed to the default risk, which is reflecting in the interest rate, at which the capital is provided to the debtor.

Both creditor and borrower suffer when the expected credit risk of the borrower is high: the lender with increased risk over the life of the loan, and the borrower with a high interest rate.

The default-risk adjusted interest rate represents the costs of borrowing of debts for any debtor and its divergence from a risk free counterparty represents the yield or credit spread.

There are a variety of available techniques (models) that are usable in the default risk measurement. Based on their common features, they can be grouped into four main categories: financial statements analysis models, external rating models, structural models and value at risk based models.

The financial statements analysis models (or scoring models) measure the default risk of the individual borrower using specific financial statement items or ratios that are quantify, using data from these statements (accounting measures of default risk). There are many variants of them and they mainly differ in their own construction, in the chosen financial ratios, in the number of financial ratios that are taken into account, next the importance of chosen ratios expressed through weightings may differ, during the process of model constructing the different mathematical and statistical methods have been used, applicability may vary etc. Except other, as well the quality, it means the ability of each model to predict the debtor’s failure, is different.

The development of financial statements analysis models (also known as prediction models for financial default) started in the late 1960’s and continues to this day. Arguably the two most influential works were those by Beaver (1966) and Altman (1968), whose models are known as Altman’s Z-scores.

As other examples may be mentioned Springate model (1978), Ohlson O-score (1980), Zmijewski model (1984), Taffler-Tissawa index (1984), Zavgren model (1985), Horrigan model (1996) etc. In the condition of the Slovak Republic, mainly methods developed in the Czech Republic are preferred because of the similarity of the national economies, such as IN models and Index of the Czech National Bank.

The external rating models provide a measure of the relative creditworthiness of the entity (mainly companies, financial institutions, and states) or specific securities, taking into account a wide range of factors, e.g. in case of corporate rating can be mentioned environmental conditions, mainly macroeconomic factors, development of the specified sector, where the rated companies belongs to, competitive position in the market, management quality, financial results, etc. Ratings are provided by rating agencies and usually have the character of letter ratings. It is applied that the higher rating the borrower has (the letter “A”), the higher is the borrower’s capacity to meet its liabilities and vice-versa. But as the Standard & Poor’s notices on its official web-site

.. rating opinions are not intended as guarantees of credit quality or the exact measures of the profitability that a particular debt issue will default. Instead, ratings express relative opinions about the creditworthiness of an issuer or credit quality of an individual debt issue, from strongest to weakest, within a universe of credit risk.

Among the most prestigious rating agencies belongs Standard & Poor’s, Fitch, and Moody’s. Ratings for the same rated entity provided by different rating agencies are usually different and each rating agency has own rating know-how, rating process and own rating scale. Rating is made on the basis of publicity available sources, internal as well as external, mainly financial statements, but also non-publicity sources (private information conveyed by the rated entity) are often taken into account.

In many ratings, within the process of determining the default risk,

the financial ratios, which measure the capacity of the rated company to meet debt payments and generate stable and  predictable cash flow

play very important role. For instance, the rating agency Standard & Poor’s uses following financial ratios.

The financial ratios used in the rating by Standard & Poor’s

Pretax interest coverage ratio Pretax return on pernament capital ratio
EBITDA interest coverage ratio Operating income / Sales
Funds from operations / Total debt ratio Long-term debt capital ratio
Free operating CF / Total debt ratio Total debt / Capitalization ratio


The structural models quantify the likelihood of the borrower’s default. As the main impulse for their formation, the foundations of modern theory of option pricing premiums presented in the works of Fisher, Scholes, and Merton during the seventies of last century can be seen. The first presented structural model was the Merton model (1974), lately were introduced Black- Cox model (1976), Geske model (1977) and currently one of the most popular Keaholfer- McQuown-Vasicek model (KMV model, 1993) etc.

In the context of the structural models, the default occurs exactly when the borrower’s assets market value is lower than the book value of borrower’s liabilities. The key assumption is that all needed and relevant information on borrower’s credit risk profile are included in the borrower’s financial statements, as well in the market prices of all securities that the borrower emitted (till that time). That the market data are incorporated, the models are more responsive to the changing conditions.

These models require determining the market value of borrower’s asset. Their market value is the response of future borrower’s opportunities, as well of information on the situation in the industry, market or overall economy. The critical credit situation may happen in more cases, e. g. change rating, restructuring of the company, bankruptcy, and when the company does not meet its liabilities or is not willing to meet them. The last three cases directly relate to the default risk.

The structural models have also some restrictions. First of all they are not applicable in general, because not in all cases the market value of assets is known. This missing information may be replaced by the information on market price of borrower’s shares. If this information is also missing, then at least the market value of some borrower’s liabilities must be known, e.g. information on bonds’ market price. If no information exists, the models cannot be used. The next is that the models are more or less “insufficient to generate meaningful default probabilities or spreads, and that the models suffer from incomplete causality”. They are also criticized that they assume exact information on the moment when the borrower fails to meet own commitments (when the default occurs), because the default is an unexpected event in the “life” of borrower.

The transition (conversion) models represent another measurement methodology of default risk. They have a base in value at risk methodology, which has become a standard tool for risk quantifying. It allows investors to calculate economic losses on a portfolio basis measuring the overall market risk. It can be defined as “the maximum potential loss in value of overall investment portfolio” (consisting from more than one kind of investment) “with a given probability over a certain time horizon”. Simply said “it is a number that indicates how much the investor can lose with defined probability over a given time horizon.” In terms of statistics “…the value of risk entails the estimation of a quantile of the distribution of returns.” There are many methods of value at risk estimation and investors usually have a great flexibility in decisions, which methods would be applied. In general, they differ in the way of simulation of changes of risk factors and in the way of transformation these changes into the changes of investment portfolio. Especially the variance and covariance method, historical simulation method and Monte Carlo simulation are used.

Value at risk based default models measure expected losses over a given time period at the defined tolerance level. In the contrast to previously mentioned structural default models, they are intended to use in analysing and managing the credit risk of total investment portfolio, rather than individual investments. This group of models consists from more other models. The CreditMetrics model can be picked up as the representative of this group.

The CreditMetrics model was developed by the bank J. P. Morgan in the nineties of the last century. Nowadays it has become one of the most popular of default risk measurement mainly due its general usage in the practise – it may be used to determine default risk in case of any type of financial liabilities, if all needed input data are known. In general, the model estimates the default of borrower based on the change of its external rating (credit quality) and thereby it is close related to the external rate models. It incorporates so-called transition matrix, which shows how likely the borrower may move from one credit grade to another based on the historical data. The transition probability table is provided by all big rating agencies. The risk of default is determined through the volatility of debt’s value, e.g. bond value, measured by the standard deviation within the given time period. This volatility is given by the possible default events, bus as well as up– and downgrades in borrower’s credit quality.

Authors Allen – Powell has presented a short but felicitous comparison of strengths and weaknesses of discussed default models.

The strengths and weakness of presented default models

Financial statments analysis models External rating models Structural models CreditMetrics
Detailed borrower’s specific financial analysis Detailed analysis of financial. Detailed analysis of financial. Only the debts and asset values. Based on external ratings that include detailed financial analysis.
Industry differentiation Most of them do not differentiate between industries. Industry factors are incorporated at time of rating. Based on market fluctuations that will vary with the industry risk. Based on ratings that incorporate industry factors at the time of rating.
Fluctuates with market (no time delays) No fluctuations with market. No fluctuations with market. Highly responsive to market fluctuations. No fluctuation with market.
Easy to model Relatively easy to duplicate models on a spreadsheets. Ratings readily available to researches. Complex techniques. Complex techniques.
Accuracy High at time of rating, lower as time passes. High at time of rating, lower as time passes. Medium – calibration can improve accuracy. High at time of rating, lower as time passes.



The investment activities are closely related to the elements of uncertainty and risk. The uncertainty in the investment process represents the impossibility of reliable determination of future factors that may affect investment returns. Then the risk of any investments may be defined as the risk that the real investment returns (cash flows) will differ from the expected. As has been noted, investor faces the whole complex of risks, which can be classified from many points of view. The identification of these risks is the basis for other steps within the investment process, mainly investment valuation.

In the presented paper, two specific kinds of risk were discussed in more details – the equity risk and default risk. To the equity risk is the investor exposed in connection with investments where no cash flows are promised, the default risk is characterized for investment with promised cash flows. Then in connection with these risks, several models of risk measurement have been presented in more details, e.g. statistical measures of risk, models used beta factor or multiple beta factors (CAPM model, arbitrage pricing model, multifactor model), proxy model, scoring models of default, external rating models, structural models and finally CreditRisk model.

Kramarova.K., Stefanikova L.